Abstract: Quantum anomalous Hall effect has been predicted in HgMnTe quantum wells with
an out-of-plane magnetization of Mn atoms. However, since HgMnTe quantum wells
are paramagnetic, an out-of-plane magnetic field is required to polarize
magnetic moments of Mn atoms, which inevitably induces Landau levels and makes
it difficult to identify the origin of the quantized Hall conductance
experimentally. In this work, we study the quantum anomalous Hall effect in the
presence of an in-plane magnetic field in Mn doped HgTe quantum wells. For a
small out-of-plane magnetic field, the in-plane magnetic field can drive the
system from a normal insulating state to a quantum anomalous Hall state. When
the out-of-plane magnetic field is slightly above the transition point, the
system shows a reentrant behavior of Hall conductance, varying from $-e^2/h$ to
0 and back to $-e^2/h$, with increasing in-plane magnetic fields. The reentrant
quantum anomalous Hall effect originates from the interplay between the
exchange coupling of magnetic moments and the direct Zeeman coupling of
magnetic fields. The calculation incorporating Landau levels shows that there
is no qualitative change of the reentrant behavior.